The decay law can have an irregular character

Within a well-known decay model describing a particle confined initially within a spherical $\delta$ potential shell, we consider the situation when the undecayed state has an unusual energy distribution decaying slowly as $k\to\infty$; the simplest example corresponds to a wave function constant within the shell. We show that the non-decay probability as a function of time behaves then in a highly irregular, most likely fractal way.Comment: 4 pages, 3 eps figure

Sufficient conditions for the anti-Zeno effect

The ideal anti-Zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system. We present a straightforward way to derive sufficient conditions under which such a situation occurs expressed in terms of the decaying states and spectral properties of the Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno effects is in fact very narrow.Comment: LatEx2e, 9 pages; a revised text, to appear in J. Phys. A: Math. Ge

Transport in simple networks described by integrable discrete nonlinear Schr\"Aodinger equation

We elucidate the case in which the Ablowitz-Ladik (AL) type discrete nonlinear Schr\"Aodinger equa- tion (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple 1-dimensional (1-d) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one (Sobirov et al, Phys. Rev. E 81, 066602 (2010)) on the continuum NLSE to the discrete case. We find: (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1-d discrete chain, but is multiplied by the inverse of square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; (3) under findings (1) and (2), there exist an infinite number of constants of motion. As a practical issue, with use of AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds

Exterior-Interior Duality for Discrete Graphs

The Exterior-Interior duality expresses a deep connection between the Laplace spectrum in bounded and connected domains in $\mathbb{R}^2$, and the scattering matrices in the exterior of the domains. Here, this link is extended to the study of the spectrum of the discrete Laplacian on finite graphs. For this purpose, two methods are devised for associating scattering matrices to the graphs. The Exterior -Interior duality is derived for both methods.Comment: 15 pages 1 figur

Late solitary bone metastasis of a primary pulmonary synovial sarcoma with SYT-SSX1 translocation type: case report with a long follow-up

Primary synovial sarcoma outside its classical presentation in para-articular soft tissue of young patients is rare but regularly reported. One of the rarest primary locations is the lung. We describe a 73-year-old female patient who presented with a solitary malignant bone tumor 8years after the resection of a lung neoplasm. The bone tumor was classified as an osteosarcoma and the lung tumor as an atypical carcinoid tumor at their first respective diagnostic work-ups. The resection of the affected humerus with allograft and endoprosthesis implantation followed. Reevaluation of the tumor samples at the time of the local recurrence of the bone tumor 6years following the initial symptoms of the bone tumor lead to the reclassification of both specimens as synovial sarcomas. Both neoplasms contained the SYT-SSX1 type of the diagnostic translocation t(X;18) as detected by the reverse-transcription polymerase chain reaction analysis. The patient died 14years after the resection of the primary synovial sarcoma of the lung and 6years following the occurrence of the bone metastasis. This prolonged clinical course is uncommon for the SYT-SSX1 translocation, which, in other locations, is usually associated with an unfavorable prognosi

The additional value of CT images interpretation in the differential diagnosis of benign vs. malignant primary bone lesions with 18F-FDG-PET/CT

Objective: To evaluate the value of a dedicated interpretation of the CT images in the differential diagnosis of benign vs. malignant primary bone lesions with 18fluorodeoxyglucose-positron emission tomography/computed tomography (18F-FDG-PET/CT). Materials and methods: In 50 consecutive patients (21 women, 29 men, mean age 36.9, age range 11-72) with suspected primary bone neoplasm conventional radiographs and 18F-FDG-PET/CT were performed. Differentiation of benign and malignant lesions was separately performed on conventional radiographs, PET alone (PET), and PET/CT with specific evaluation of the CT part. Histology served as the standard of reference in 46 cases, clinical, and imaging follow-up in four cases. Results: According to the standard of reference, conventional 17 lesions were benign and 33 malignant. Sensitivity, specificity, and accuracy in assessment of malignancy was 85%, 65% and 78% for conventional radiographs, 85%, 35% and 68% for PET alone and 91%, 77% and 86% for combined PET/CT. Median SUVmax was 3.5 for benign lesions (range 1.6-8.0) and 5.7 (range 0.8-41.7) for malignant lesions. In eight patients with bone lesions with high FDG-uptake (SUVmax ≥ 2.5) dedicated CT interpretation led to the correct diagnosis of a benign lesion (three fibrous dysplasias, two osteomyelitis, one aneurysmatic bone cyst, one fibrous cortical defect, 1 phosphaturic mesenchymal tumor). In four patients with lesions with low FDG-uptake (SUVmax < 2.5) dedicated CT interpretation led to the correct diagnosis of a malignant lesion (three chondrosarcomas and one leiomyosarcoma). Combined PET/CT was significantly more accurate in the differentiation of benign and malignant lesions than PET alone (p = .039). There was no significant difference between PET/CT and conventional radiographs (p = .625). Conclusion: Dedicated interpretation of the CT part significantly improved the performance of FDG-PET/CT in differentiation of benign and malignant primary bone lesions compared to PET alone. PET/CT more commonly differentiated benign from malignant primary bone lesions compared with conventional radiographs, but this difference was not significan

The influence of tumor- and treatment-related factors on the development of local recurrence in osteosarcoma after adequate surgery. An analysis of 1355 patients treated on neoadjuvant Cooperative Osteosarcoma Study Group protocols

Background: Local recurrence (LR) in osteosarcoma is associated with very poor prognosis. We sought to evaluate which factors correlate with LR in patients who achieved complete surgical remission with adequate margins. Patients and methods: We analyzed 1355 patients with previously untreated high-grade central osteosarcoma of the extremities, the shoulder and the pelvis registered in neoadjuvant Cooperative Osteosarcoma Study Group trials between 1986 and 2005. Seventy-six patients developed LR. Results: Median follow-up was 5.56 years. No participation in a study, pelvic tumor site, limb-sparing surgery, soft tissue infiltration beyond the periosteum, poor response to neoadjuvant chemotherapy, failure to complete the planned chemotherapy protocol and biopsy at a center other than the one performing the tumor resection were significantly associated with a higher LR rate. No differences were found for varying surgical margin widths. Surgical treatment at centers with small patient volume and additional surgery in the primary tumor area, other than biopsy and tumor resection, were significantly associated with a higher rate of ablative surgery. Conclusions: Patient enrollment in clinical trials and performing the biopsy at experienced institutions capable of undertaking the tumor resection without compromising the oncological and functional outcome should be pursued in the futur

Spectral properties of quantized barrier billiards

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions, number variances, spectral form factors, and the level dynamics is carried out. For a special member of the billiard family, the form factor is calculated analytically for small arguments in the diagonal approximation. All results together are consistent with the so-called semi-Poisson statistics.Comment: 8 pages, 9 figure

Green functions for generalized point interactions in 1D: A scattering approach

Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of $N$ general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.Comment: Revtex, 9 pages, 3 EPS figures. To be published in PR

Electron focusing, mode spectroscopy and mass enhancement in small GaAs/AlGaAs rings

A new electron focusing effect has been discovered in small single and coupled GaAs/AlGaAs rings. The focusing in the single ring is attributed solely to internal orbits. The focusing effect allows the ring to be used as a small mass spectrometer. The focusing causes peaks in the magnetoresistance at low fields, and the peak positions were used to study the dispersion relation of the one-dimensional magnetoelectric subbands. The electron effective mass increases with the applied magnetic field by a factor of $50$, at a magnetic field of $0.5T$. This is the first time this increase has been measured directly. General agreement obtains between the experiment and the subband calculations for straight channels.Comment: 13 pages figures are available by reques